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Mohammadipour, Maryam (2013)
Languages: English
Types: Doctoral thesis
April 2009 This PhD thesis focuses on using time series models for counts in modelling and forecasting a special type of count series called intermittent series. An intermittent series is a series of non-negative integer values with some zero values. Such series occur in many areas including inventory control of spare parts. Various methods have been developed for intermittent demand forecasting with Croston’s method being the most widely used. Some studies focus on finding a model underlying Croston’s method. With none of these studies being successful in demonstrating an underlying model for which Croston’s method is optimal, the focus should now shift towards stationary models for intermittent demand forecasting. This thesis explores the application of a class of models for count data called the Integer Autoregressive Moving Average (INARMA) models. INARMA models have had applications in different areas such as medical science and economics, but this is the first attempt to use such a model-based method to forecast intermittent demand. In this PhD research, we first fill some gaps in the INARMA literature by finding the unconditional variance and the autocorrelation function of the general INARMA(p,q) model. The conditional expected value of the aggregated process over lead time is also obtained to be used as a lead time forecast. The accuracy of h-step-ahead and lead time INARMA forecasts are then compared to those obtained by benchmark methods of Croston, Syntetos-Boylan Approximation (SBA) and Shale-Boylan-Johnston (SBJ). The results of the simulation suggest that in the presence of a high autocorrelation in data, INARMA yields much more accurate one-step ahead forecasts than benchmark methods. The degree of improvement increases for longer data histories. It has been shown that instead of identification of the autoregressive and moving average order of the INARMA model, the most general model among the possible models can be used for forecasting. This is especially useful for short history and high autocorrelation in data. The findings of the thesis have been tested on two real data sets: (i) Royal Air Force (RAF) demand history of 16,000 SKUs and (ii) 3,000 series of intermittent demand from the automotive industry. The results show that for sparse data with long history, there is a substantial improvement in using INARMA over the benchmarks in terms of Mean Square Error (MSE) and Mean Absolute Scaled Error (MASE) for the one-step ahead forecasts. However, for series with short history the improvement is narrower. The improvement is greater for h-step ahead forecasts. The results also confirm the superiority of INARMA over the benchmark methods for lead time forecasts.
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    • Appendix 3.A Autocorrelation Function of an INARMA(1,1) Model......................... 272 Appendix 3.B The Unconditional Variance of an INARMA(p,q) Model .................... 274 Appendix 3.C The Cross-Covariance Function between Y and Z for an INARMA(p,q) Model............................................................................................................................. 280 Appendix 3.D Over Lead Time Aggregation of an INAR(1) Model ........................... 281 4.5264 3.3006 3.4328 0.5062 1.4508 0.4504 0.4853 1.2606 3.6386 0.5676 1.1517 2.6916 2.8464 0.4086 0.4502 1.4470 0.3257 4.4325 2.6883 0.4286 0.4490 1.3820 1.4718 2.8394 0.4185 0.4541 1.3907 0.5326 1.3271
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